2(x-4)-(x-2)=(x+2)(x-4)

Solution for 2(x-4)-(x-2)=(x+2)(x-4) equation:

Simplifying
2(x + -4) + -1(x + -2) = (x + 2)(x + -4)

Reorder the terms:
2(-4 + x) + -1(x + -2) = (x + 2)(x + -4)
(-4 * 2 + x * 2) + -1(x + -2) = (x + 2)(x + -4)
(-8 + 2x) + -1(x + -2) = (x + 2)(x + -4)

Reorder the terms:
-8 + 2x + -1(-2 + x) = (x + 2)(x + -4)
-8 + 2x + (-2 * -1 + x * -1) = (x + 2)(x + -4)
-8 + 2x + (2 + -1x) = (x + 2)(x + -4)

Reorder the terms:
-8 + 2 + 2x + -1x = (x + 2)(x + -4)

Combine like terms: -8 + 2 = -6
-6 + 2x + -1x = (x + 2)(x + -4)

Combine like terms: 2x + -1x = 1x
-6 + 1x = (x + 2)(x + -4)

Reorder the terms:
-6 + 1x = (2 + x)(x + -4)

Reorder the terms:
-6 + 1x = (2 + x)(-4 + x)

Multiply (2 + x) * (-4 + x)
-6 + 1x = (2(-4 + x) + x(-4 + x))
-6 + 1x = ((-4 * 2 + x * 2) + x(-4 + x))
-6 + 1x = ((-8 + 2x) + x(-4 + x))
-6 + 1x = (-8 + 2x + (-4 * x + x * x))
-6 + 1x = (-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
-6 + 1x = (-8 + -2x + x2)

Solving
-6 + 1x = -8 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 8 + 1x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: -6 + 8 = 2
2 + 1x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: 1x + 2x = 3x
2 + 3x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Reorder the terms:
2 + 3x + -1x2 = -8 + 8 + -2x + 2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
2 + 3x + -1x2 = 0 + -2x + 2x + x2 + -1x2
2 + 3x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
2 + 3x + -1x2 = 0 + x2 + -1x2
2 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -3x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x + x2 = 0 + 2
-3x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3x + x2 = 2

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 2 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3x + x2 = 4.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + -1.5 = 2.061552813

Simplifying
x + -1.5 = 2.061552813

Reorder the terms:
-1.5 + x = 2.061552813

Solving
-1.5 + x = 2.061552813

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.061552813 + 1.5
x = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
x = 3.561552813

Simplifying
x = 3.561552813

Subproblem 2
x + -1.5 = -2.061552813

Simplifying
x + -1.5 = -2.061552813

Reorder the terms:
-1.5 + x = -2.061552813

Solving
-1.5 + x = -2.061552813

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.061552813 + 1.5
x = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
x = -0.561552813

Simplifying
x = -0.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.561552813, -0.561552813}